Philosophy 251: Handout #4

VII. Determine the truth value of each of the following formulas, given that the truth values of the atomic formulas are as follows--P = F, Q = T, R = T.

1. ~[~P v ( ~ Q v ~R )]
2. ( P Q ) v ( Q R )
3. ( P Q ) v ( Q ~R )
4. ~[~P ~( R ~ [ P ( Q & R )])]
5. ~( R ~P ) & [ Q ( P & R )]

VIII. Construct complete truth tables for each of the following formulas. For each formula determine whether the formula is contingent, a tautology, or a contradiction.

1. A ( B A )
2. ( ~F & ~ G ) v ~( F v G )
3. ~[[( P v Q ) & ( Q v R )] & (~P & ~ R)]
4. ( M ~M ) & ( N O )
5. ( S v ~T ) ~~( T S )

IX. For each of the following pairs of formulas determine whether imples , implies , or whether and are logically equivalent.

1. ~( A & B )	~( A v B )	4. C ( D C )	( C & ~C ) v ( E E )
2. X ( ~X X )	~ ( X ~X )	5. ~( O & P ) ( P ~R )	( O & P ) ~R
3. Q v ~ ( S v ~T )	( Q~ T ) v S

X. For each of the following arguments, construct a truth table to determine whether the argument is valid or invalid.

1. A ( B & C ), B C, ~B / ~A
2. D v ( E & ~ F ), ( F E )  D, ~D v F / ~( E v F )
3. ~( J K ), ~J, ~K / L & ~L
4. ( M N ) ( N  O ), N / M O
5. [( U & W ) & X ] v ( ~U ~X ), U W, W X / W  X